Can I hire a shredding company under HIPAA for my records?

Yes, you absolutely can hire a third party to assist in destroying your unneeded patient records, including protected health information under HIPAA, however, the third party would most certainly qualify as a business associate, requiring a business associate agreement to be executed governing the treatment of the records. Make sure you are indemnified for any breaches by the third party, just in case their shredder jams and they opt for a quick public dump of records!